Unit testing is essential for software quality assurance, yet writing and maintaining tests remains time-consuming and error-prone. To address this challenge, researchers have proposed techniques for automating unit test generation, including heuristic-based methods and more recent approaches that leverage large language models (LLMs). However, these approaches are inherently path-insensitive because they rely on fixed heuristics or limited contextual information and fail to reason about deep control-flow structures, which leads to inadequate coverage, especially for deep execution paths. JUnitGenie extracts code knowledge from Java projects, distills it into structured prompts, and guides LLMs to generate highcoverage tests. We evaluate JUnitGenie on 2,258 complex focal methods from ten real-world Java projects. Results show that JUnitGenie improves branch coverage by an average of 29.60% and line coverage by 31.00% over both heuristic and LLM-based baselines, and generalizes effectively across both closed- and open-source foundation models. JUnitGenie is available at https://github.com/DianshuLiao/JUnitGenie-ICSE-Demo, and the demo video is available at https://www.youtube.com/watch?v=-jWJaf661mw.